Abstract

Radiances observed by the GOES-VAS 6.7 um channel are compared to computations
from simultaneous soundings of temperature and moisture. The soundings were
measured using high precision instruments aboard the NCAR Sabreliner during
ERICA, over Edmonton, Alberta, and over Champaign, IL. Three radiation codes
are used to simulate the satellite observations, a narrow band model and two
line-by-line codes, FASCODE2 and the Goddard Laboratory for Atmospheres
line-by-line model (GLA-LBL). This comparison shows that all three models
overestimate the observed brightness temperatures but reproduce the full range
in observed brightness temperatures. Possible sources for this bias are
investigated, such as transmission through a cloudy lower boundary, scattering
by thin high-level cirrus, and water vapor continuum absorption. It is
concluded that no one mechanism can alone account for the observed
discrepancies.

Increasing awareness of the role of upper-tropospheric water vapor in climate
has emphasized the importance of its measurement and of understanding the
radiation field of the upper troposphere (Starr and Melfi, 1991; Lindzen, 1990;
Rind et al., 1991). The operational radiosonde network does not produce
reliable moisture information above 500mb (Elliott and Gaffen, 1991; Gaffen et
al., 1991), and, unless hygrometer modifications are made in the near future,
global monitoring of upper-tropospheric moisture must rely on satellite remote
sensing techniques. Infrared sounding is the most developed technique for
upper-tropospheric water vapor measurements, but it will be increasingly
complimented by other remote sensing techniques (e.g. passive microwave
sounding (Schuessel and Emery, 1990; Tjemkes et al., 1991), SAGE solar
occultation observations (McCormick et al., 1993), and lidar (Melfi et al.,
1989; Browell et al., 1979; Cahen et al., 1982)). Methods for deriving
soundings of atmospheric moisture from passive infrared radiance observations
have been improving for many years (Smith et al., 1979; Chedin et al., 1985;
Hayden1988), and radiance data for sounding purposes are collected by the VAS
system on GOES satellites (Smith, 1983) and the TOVS system on NOAA polar
orbiters (Susskind 1993). These measurements will be improved considerably in
the next generation of GOES satellites (Starr and Melfi, 1991).
Upper-tropospheric moisture estimates derived from these infrared radiances
depend upon observations of radiation emitted in the strong 6.5 um
vibrational-rotational band of water vapor. Most satellite sounding systems
include a channel that measures radiance at about 6.7 um, which detects
radiation emitted by water vapor above 400mb.

Given the paucity of reliable in situ moisture measurements above 500mb,
it is difficult to assess the modeling of upper-tropospheric radiative
processes from which satellite moisture profiles are derived. In this paper,
we present precise temperature and moisture profiles collected from the NCAR
Sabreliner during two recent field projects. We compute radiances from these
soundings using three independent radiation codes for comparison to
simultaneous observations from the GOES-VAS 6.7 um channel. These comparisons
test the validity of radiation codes and satellite observations and, by
extension, the ability to accurately infer water vapor concentrations from
satellite observations.

Most previous attempts to compute satellite radiances using balloon soundings
of temperature and moisture yielded poor results for channels in the strongly
absorbing 6.5 um water vapor band (i.e. 6.7 um and 7.2 um channels) (Poc et
al., 1980; Chesters et al., 1985; Hayden, 1988). Hayden (1988), for example,
computed GOES-VAS channel 10 (6.7 um) brightness temperatures that overestimate
the observations by an average of 5.27 K, with a correlation to the
observations of only 0.59. Menzel et al. (1981), on the contrary, found good
correspondence between observed and computed brightness temperatures for the
same channel. It is not clear, however, what assumptions went into the Menzel
et al. (1981) calculation and whether an adjustment was made to the
transmission function for this channel as is traditional in VAS analysis
(Hayden, 1988). Satellite radiance observations in the water vapor channels
are sensitive to moisture at levels above where the balloon instrument is
reliable, so the uncertainty in the moisture profiles of these earlier studies
limits a useful comparison of the computed and observed radiances. To compute
radiances in channels where carbon dioxide is the principal absorber, only the
temperature profile must be measured, which is quite accurately accomplished by
radiosondes. Chesters et al. (1985) compared computed and observed brightness
temperatures from the VAS channels that depend only on atmospheric temperature
and found agreement to within +/-1 K. The aircraft-based moisture measurements
used in the present study should eliminate some of the uncertainties that were
unavoidable in the earlier balloon-based studies of radiances in the VAS water
vapor channel.

The data used in this paper are soundings of the atmospheric temperature and
moisture measured from the NCAR Sabreliner and 6.7um radiances observed by the
VAS instrument on the GOES-7 satellite.

a) Aircraft Data

During two recent field projects we conducted detailed soundings of the upper
troposphere and lower stratosphere from the NCAR Sabreliner. Temperature was
measured with a Rosemont platinum resistance sensor with accuracy of 1 K,
resolution of 0.006 K, and response time of 0.1s (see NCAR-RAF Bulletins 3 and
9). Moisture was measured with a newly developed frostpoint hygrometer. The
rapid response and large range of this hygrometer is accomplished by using a
cryogenically cooled mirror (Spyers-Duran, 1990). This cryogenic hygrometer
responds at about 1s, resolves 0.05 K variations in frost point, and has a
frost point range of -10deg.C to -90deg.C. Cloud particle concentration was
measured by a forward scattering spectrometer probe (FSSP) that detects the
concentration and size distribution of cloud particles.

Twelve vertical atmospheric profiles were extracted from the data. The
soundings generally extend to an altitude of 12 km into the lower stratosphere.
Above this altitude, there is very little water vapor (Mastenbrook, 1980;
Ellsaesser, 1983), and hence little contribution to the outgoing radiance near
6.7 um. For the purposes of radiative transfer calculations, the profiles of
temperature and moisture were extrapolated to an altitude of 100 km. The lower
boundary for the radiative transfer may be either the surface or a cloud. When
a cloud is present in the profile, its altitude and temperature were judged
using the IR window channel brightness temperature and the observed temperature
profile, this process will be described fully below.

b) Evaluation of Water Vapor Measurement

The accuracy of the hygrometer is critical to this study and an attempt was
made verify the NCAR-RAF specifications given above. Under ice-saturated
conditions, the frostpoint should equal the ambient temperature, so the
frostpoint observed in deep cold clouds provides an in situ calibration
of the hygrometer against the temperature probe.

We conducted a series of soundings with the Sabreliner in conjunction with the
release of Vaisala radiosondes. The results from one set of soundings are
shown in figure 2. During these soundings, the aircraft passed within 4 km of
the balloon launch site and the balloon was released midway in the aircraft
descent. The regions marked as cloudy were determined both by the FSSP and by
sight. Assuming the atmosphere was saturated with respect to ice within the
cloud regions, the Vaisala sonde appears more accurate at low levels, the two
agree at mid troposphere, and the cryogenic hygrometer is more accurate in the
upper troposphere. The cryogenic hygrometer generally does not respond well at
frost points above about -20[[ring]]C; also the lowest segment of the aircraft
sounding was taken during an unusually rapid descent due to deteriorating
weather conditions, and hence the cryogenic hygrometer may not have been able
to respond quickly enough to the rapid moistening as the aircraft passed
through the cloud. In cases where the cryogenic hygrometer measurement is
clearly bad at low altitudes, the frost point is substituted with the value
from a conventional chilled mirror hygrometer also aboard the aircraft. In
very dry cold air (below -40[[ring]]C) in the upper troposphere, the frost
point depression (ambient temperature minus frostpoint) measured by the humicap
sensor becomes nearly constant as the instrument appears to respond more to the
ambient temperature than to the features in the moisture profile.

c) Satellite Data

The VAS channel 10 is referred to as the 6.7 um or water vapor (WV) channel
since its filter function is centered at a wavelength of 6.725 um (or
wavenumber 1487.0 cm[-1]) in the 6.5 um
vibrational-rotational absorption band of water. (See for example, Montgomery
and Uccellini, 1985 and Chesters et al., 1982 for a detailed description of the
GOES-VAS system.) Figure 3 shows the WV channel filter function along with a
high resolution spectrum of radiance computed using the Goddard Laboratory for
Atmospheres line-by-line code and a typical aircraft profile.

The sloping aircraft soundings will cross many satellite image pixels as the
aircraft travels horizontally. Figure 4 shows a typical example of the
brightness temperature observed over the track of an aircraft sounding from the
hourly images spanning the flight time. There are slight variations in the
atmosphere over this distance and time, on the order of +/-2 K. For comparison
with the computed radiance, the mean brightness temperature over the upper
tropospheric section of the aircraft track from the image closest in time to
the sounding is chosen.

In this paper we will also consider the GOES-7 channel 8 or IR window
observations of radiances at 11.170 um (895.3 cm[-1]).
Since the atmosphere is nearly transparent at this wavelength, this channel
gives the temperature of the opaque lower boundary for the radiative transfer
calculation. This technique introduces errors that will be discussed in the
next section.

The 6.7 um radiances are computed as described in, for example, Liou, 1980.
In this paper, radiances will be expressed in terms of brightness temperature.
The computed brightness temperature is the inverse Planck function evaluated at
the center wavenumber of channel 10 ([[nu]]=1487.0cm[-1]).
Given an accurate profile of the atmospheric temperature and humidity, the
difficulties in computing the brightness temperature are in estimating the
surface term and modeling the transmissivity. These two terms are the subjects
of the next two sub-sections.

The zenith angle is found geometrically from the positions of the satellite and
sounding location. GOES-7 is the only remaining geostationary satellite in
orbit over the U.S., it is shuttled between positions over the East and West
coasts depending upon the season. Thus, during the ERICA project the
satellite's viewing angle changed each day and its daily position must be taken
into account. The range of zenith angles in this investigation is from
44[[ring]] to 57[[ring]].

a) Clear Atmosphere Transmission

In this study we use three independent atmospheric transmission models. The
first is a narrow band model (NBM) that uses the Goody random line
parameterization and the Curtis-Godson parameterization for the dependence of
the line parameters on temperature and pressure (Goody and Young, 1989; Rodgers
and Walshaw, 1966). The NBM is an approximate method for radiative transfer
that although not as accurate as other methods, gives high spectral resolution
and very fast computational speed. The second model is FASCODE2 (Fast
Atmospheric Signature Code), a line-by-line code available from AFGL (Clough et
al., 1981, 1992). The third model was developed at the NASA Goddard Laboratory
for Atmospheres (GLA) (Ridgeway et al., 1991) snf also uses line-by-line
calculations. The two line-by-line codes both use the HITRAN86 spectral data
as well. An important difference between the two models is in the treatment of
continuum absorption and line shape (Clough, 1992). The inclusion of this
effect in FASCODE2 should yield lower brightness temperatures compared to the
GLA model.

b) Lower Boundary

The atmospheric profiles selected from the aircraft data were chosen so that
the atmospheric column may be assumed clear above a solid lower boundary that
may be either the ground, sea surface, or a low cloud. The temperature of the
lower boundary is taken from the GOES IR window channel brightness
temperature, TIR, and its altitude, zIR, is judged by comparing
this temperature to the aircraft sounding. There are several ways this can
introduce errors into the calculated radiances. 1) If water vapor continuum
absorption reduces the radiance in the atmospheric window, then TIR
will be too low and zIR too high (assuming decreasing temperature
with height). 2) The boundary may not emit as a black body. 3) If the cloud
top is thin, the effective boundary may not be well defined, and TIR
will be warmer than the actual cloud top (where the cloud particle
concentration goes to zero).

When the lower boundary is land or cloud (as opposed to sea surface), its
emission may differ from that of a black body, and may be described by
I(nu,z0)=epsilon*B(nu,T0)
where epsilon is the emissivity of the surface (potentially dependent on
wavenumber) and T0 and z0 are the actual boundary conditions.
The emissivity of a cloud depends on the scattering processes in the cloud and
can be related to the Mie parameters by an analytic two-stream solution
of the scattering radiative transfer equations (see Salathe and Smith 1994).

Assuming the lower boundary radiates as a black body at the IR window
brightness temperature introduces an error when the emmissivity is not one,
and especially when
the boundary is an elevated cloud top. This problem is treated by considering
radiative transfer in a cloudy atmosphere as described in the next section.

c) Cloudy Atmosphere Transmission

The scattering of radiation in the infrared window by high clouds is well
known. It is likely that the atmospheric columns for which we computed
radiances are contaminated by thin cirrus. In order to study the influence of
cloud scattering and absorption processes upon the computed 6.7 um brightness
temperatures, these effects were included in the radiative transfer
calculations for idealized cases; the results are discussed below. The
transfer of radiation in an absorbing and scattering atmosphere was computed
using a multiple scattering model as described in Salathe and Smith (1994).

The first problem introduced by cloud scattering occurs when the observed IR
channel brightness temperature does not correspond to ambient temperatures at
the cloud top as observed from the aircraft, which indicates the cloud either
is not opaque to infrared radiation or is not emitting as a black body. This
is the case with sounding E017 in Figure 5; a thin cloud was observed in this
sounding with particle concentrations ~2 cm[-3]. The
observed IR brightness temperature of 239 K corresponds to the ambient
temperature at about 6 km, which is 2 km below the cloud top (Table 1). The
results of our calculations indicate that the black-body assumption in fact
underestimates the WV channel brightness temperature.

The second problem introduced by clouds is the possibility of undetected thin
cirrus contaminating what is assumed to be a clear atmospheric path. For
example, sounding e044 (Figure 7) was conducted downwind of a dense warm-front
cirrus cloud. While no cloud particles were detected in this sounding, it does
contain several very moist and well mixed layers that may contain ice particles
either at concentrations and sizes below the instrument threshold or in other
regions of the satellite image pixel. Thus it seems that undetected cirrus
clouds do not influence the WV channel brightness temperature by more than
2K.

The brightness temperatures observed over the aircraft soundings were simulated
as described above. The technique was to assume a clear air column over a
black lower boundary. The lower boundary temperature was taken from the
corresponding IR window channel pixel, and its height judged by comparing this
temperature to the aircraft temperature sounding. Table 1 summarizes the
results of this comparison study. This table presents the satellite and
aircraft lower boundary conditions, type of lower boundary, and the brightness
temperatures observed by GOES and computed by each of the models.

In Figure 9 the computed brightness temperatures are plotted against the GOES
observations. The thick lines show the linear trend of the results of each
model, and the thin line indicates where computed and observed values are
equal. The linear correlation for each set of computed values, shown in Table
2, is quite high and the slopes are nearly one. For each model, however, the
computed brightness temperatures are on average greater than the observed
brightness temperatures. FASCODE2 radiances reproduce the GOES observations
best with the narrow band model giving the largest disparity. For all three
models, the average difference or bias between computed and observed brightness
temperatures is positive. This bias implies that the aircraft humidity
measurements indicate a drier atmosphere than would be inferred from the
satellite observation, or that the atmosphere is more opaque than indicated by
the models. The bias in the FASCODE2 computations of 3.64 K is only slightly
better than the 5.27 K bias found by Hayden (1988); the scatter, however, is
significantly reduced.

The standard deviation of the bias in Table 2 is the deviation of the
differences between individual computed and observed values from the mean bias.
For each model, the bias is larger than its standard deviation. Furthermore,
the deviations are nearly the same for each set of model results, and are
comparable to the +/-2 K misalignment error estimated from Fig. 4 (Section 2c).
It is likely, therefore, that the scatter is due to random errors such as a
misalignment of aircraft sounding and satellite observation, and are not model
dependent.

The only significant process with a known systematic influence that has been
neglected in these calculation is oxygen continuum absorption, and its
inclusion would reduce the bias in each model by about 0.5 K (see discussion in
section 3a). Applying this correction for oxygen continuum and methane
absorption to the results yields a bias of 3.1 K for FASCODE, 5.0 K for the GLA
model, and 7.4 K for the NBM.

Comparing the entries in Table 1 indicates that cases with agreement in the IR
and aircraft derived lower boundary (E017, E054, E072, E083, E084) give on
average better agreement between computed and observed brightness temperatures.
The average difference between the FASCODE and GOES brightness temperatures for
these five cases is only 2.08 K compared to 3.64 K for all cases. The bias
shows no clear relationship to boundary height. Thus, it is unlikely that
errors in the boundary emission are at fault, since these errors become small
when the boundary is low and its radiative contribution diminishes relative to
the atmospheric emission.

Of the radiation models considered here, only FASCODE included water vapor
continuum absorption at 6.7 um. Since the results from FASCODE are
considerably better than for the other two models, and continuum absorption is
the most important difference between FASCODE and the GLA model, it seems
likely that continuum absorption is significant in the upper troposphere and
in the vibrational band of water vapor. Comparison with the bias of the GLA
results (Table 2) and with FASCODE computations with the continuum absorption
suppressed, indicates that the continuum in FASCODE reduces the outgoing
brightness temperature by about 1-2 K. This difference is seen also for the
U.S. Standard Atmosphere calculation in Appendix A. This disparity is
certainly smaller than the observed bias. Given the lack of observational
verification of water vapor continuum absorption models, however, it is
possible that future improvements in the modeling of continuum absorption may
yield changes of this magnitude. Thus, in combination with other effects (such
as cloud particle absorption), improvements in modeling continuum absorption
may reduce the disagreement with satellite observations.

One way to express the magnitude of the radiance bias is to determine, assuming
our radiance calculations are perfect, the amount of additional water vapor
needed to reduce the calculated radiances to the observed values. A full
doubling of the specific humidity is required. This moisture concentration
adjustment lies well outside the error in our hygrometer and in some cases
gives super-saturated air. Thus, this means of expressing the bias does not
help to explain it but rather indicates its significance and the potential
problems in determining moisture from radiance observations.

Table 2. Summary of statistics for each model (the corrected bias includes the
effect of oxygen and methane absorption)

There is a positive bias between observed and computed WV channel radiances for
each of the radiation models used in this study. A number of assumptions and
sources of error enter the computation that may contribute to this bias:

Non-Black Lower Boundary. The assumption that the lower boundary radiates
like a black body at the IR window channel brightness temperature was discussed
in sections 3 and 4. This technique was found to cancel the unmodeled
radiative effects at a cloud top. If the emissivity of the boundary is in fact
much smaller at 6.7 um than at 11.2 um, then this assumption may contribute to
the bias, but there is no reason to believe the emissivities take such
values.

Neglect of trace gas absorption. The exclusion of gaseous constituents
other than water vapor was made after finding their influence to be less than
0.5 K. O2 absorption constituted the bulk of the 0.5 K reduction. Recent
measurements of the collision-induced absorption by O2 (Orlando et al., 1991)
have shown that earlier parameterizations (Timofeyev and Tonkov, 1978)
overestimate this effect, so it is unlikely that the O2 contribution is any
greater.

Misalignment of observations. Errors arising from misalignment of the
satellite observations and the aircraft soundings would neither be systematic
nor to amount to as much as 5 K.

Transmission model. The results from the three models are quite close, and
FASCODE and GLA have been extensively tested against other radiation models
(Ellingson, 1991). Hence these results are as accurate as possible given
present knowledge of radiative transfer in clear air (but see #8 below)

Satellite calibration. The present GOES satellite radiometer is calibrated
against a hot source and space (Chesters et al., 1982). The space reference is
considerably outside the range of observations so there may be some uncertainty
in the calibration. While the 6.7 um channel is essentially impossible to
operationally ground truth, the other channels are verified (Chesters et al.,
1985; Hayden, 1988), and since the same radiometer is used for all channels it
is unlikely to be severely in error.

Cryogenic hygrometer. This instrument has been discussed above, and it is
highly unlikely to be reporting moisture levels in error by the amount
indicated by the bias.

Zenith angle. The computed radiance depends on the zenith angle to the
satellite, which varied daily during ERICA. The satellite position was fixed
during Edmonton, so the lack of any difference in the comparisons from the two
projects indicates that an error in the zenith angle is not significant. At
mid-latitude values of the zenith angle, the sensitivity of the computed
brightness temperature is about 0.1 K for a degree of angle.

Continuum absorption. The theory and measurement of water vapor continuum
absorption is area of ongoing research (Grant, 1990; Aref'yev, 1991) and there
is much variation in how it is modeled in radiation codes. As discussed above,
the difference in the GLA and FASCODE results indicates advances in modeling
continuum absorption is unlikely to account for the full bias in computed
radiances, but may be significant in combination with other effects. The
results in this paper do not allow an assessment of the modeling of continuum
absorption, but they do make clear that this process is essential to properly
modeling upper-tropospheric radiation.

Scattering by thin high clouds. The effects of clouds on the radiation have
been neglected in computing the brightness temperatures in Table 1 since the
only detected clouds in the soundings presented were assumed to be opaque and
to form the lower boundary. As discussed above, the possibility of thin high
clouds escaping detection is quite real. However, the simple scattering
calculations presented in section 3c indicated that for thin cirrus to have a
significant effect on the WV channel radiance, they would be quite evident in
the IR channel images. But this may reduce the bias in combination with other
effects.

Table 3 summarizes several of these sources of uncertainty and the likely
magnitude of their influence on the computed brightness temperature. A
negative value indicates that the error or assumptions in the calculations tend
to underestimate the brightness temperature, and positive values indicate an
overestimate. It must be concluded that no one mechanism accounts for the
discrepancy between the observed and computed radiances. Several of the
mechanisms discussed above may combine to produce the bias; alternatively, one
mechanism may be much greater than we currently understand it to be.

In conclusion, state-of-the-art radiation codes predict considerably higher
outgoing radiances at 6.7 um than are observed from space by the GOES
satellite. After taking into account the systematic effect of additional trace
gas absorption, FASCODE yields brightness temperatures on average 3.1 K too
high, the GLA model 5.0 K too high, and the NBM 7.3 K too high. These results
reflect the varied capabilities of the three radiative transfer models.
FASCODE and the GLA model employ line-by-line calculations, and are often taken
as standards for radiative transfer calculations. The disparity between these
two codes is most likely attributable to water vapor continuum absorption,
which is not accounted for in the GLA model.

Assuming that the moisture and temperature profiles are correctly measured and
that the satellite observations are correct, the atmosphere is more opaque than
the radiation models indicate. If water vapor is the only absorber, its
upper-tropospheric concentration would have to be doubled to produce the
opacity in the radiation models needed to match the satellite observations.
Since FASCODE yields excellent agreement with observations of downwelling
radiance (Smith, 1990), the problem seems to be unique to modeling the
radiative properties of the upper troposphere in the strongly absorbing water
vapor vibrational band.

Inaccurate modeling of the radiation field at this altitude and wavelength has
implications for both modeling and monitoring climate change. While the
observations used in this study do not allow a resolution of the problem, the
results suggest possible mechanisms that may enhance the opacity of the upper
troposphere. These are absorption of radiation by trace gases and non-gaseous
material (ice and other aerosol) and water vapor continuum absorption.
Uncertainties in these processes and in upper-tropospheric radiation in general
must be resolved before we can confidently move forward in modeling and
monitoring upper-tropospheric moist and radiative processes and their effects
on the climate.

Acknowledgments

Paul Gluhosky at Yale played an invaluable role in supporting our research
during the field projects and in developing software to view and analyze the
aircraft and satellite data. Jielun Sun's earlier work at Yale in radiative
transfer made many aspects of this work easier. Dave Kratz at NASA/GSFC
supplied the Goody random line parameters and useful suggestions in developing
the NBM. Bill Ridgeway of Applied Research Corp. (ARC) made the GLA
line-by-line code available. The NCAR/RAF pilots and research staff ably
supported our field projects. Jim Warnock and his colleagues at NOAA/ERL
conducted the Vaisala soundings. The GOES-VAS data were provided by the Space
Science and Engineering Center and the University of Wisconsin. This work was
supported under NSF Atmospheric Science Division grant ATM-912390 and DOE/NIGEC
grant DE-FC03-90ER61010, and the first author was supported by a NASA Global
Change Research Fellowship.